Characteristic Classes

Abstract

AbstractLet G be a Lie group with Lie algebra g and let P be a principal G-bundle over a manifold M, with projection π : P → M. As in the paragraph preceding (6.8), let θ be a connection form in P, with curvature form Ω. We begin with the formulation in Theorem 13.1 of a basic result of André Weil [74], which states that there is a canonical homomorphism, which assigns to each conjugacy invariant polynomial on 9 a de Rham cohomology class of M, which, roughly speaking, is obtained by substituting the curvature form in the polynomial. The resulting cohomology classes in M are the characteristic classes in the title of this chapter.KeywordsVector BundleCohomology ClassNormal BundleChern ClassCurvature FormThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.